i am working on a Linux box (via ssh), which is currently completing a very time-consuming task. How can I go to sleep (close my local terminal windows) without interrupting the execution of that task?

The best way would be to use screen to create a detatchable screen run your command then detach, you can then close the original session without issue. The oldschool way would be to use nohup and send it to the background i.e. nohup <command> <args> &

screen is definitely the way to go. After detaching the screen, you can reattach it and continue to watch the progress of your task. You can also have multiple windows in a screen, to watch multiple processes.
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WeboideJul 20 '10 at 23:38